Why are Balmer lines strong in the spectra of medium-temperature stars and weak in the spectra of hot and cool stars?

Integrate the first equation over all wavelengths to find an expression for the total luminosity of a black body star. (See the second equation for a hint)

The three most prominent spectral lines of hydrogen are H-α at 656 nm, H-β at 486 nm, and H-γ 434 nm. If we observe an object with H-α at a wavelength of 700 nm, what wavelength will we observe H-β and H-γ? Is the object moving toward or away from us, and how do you know? Suppose we observe another object with H-α at 585 nm. Is this object moving toward or away from us? Is it moving slower or faster than the first object?

At rest hydrogen has a spectral line at 149nm. If this line is observed at 144 nm for the star proxima how fast is proxima moving in km/s